Search results for: Dynamic Address Allocation

Authors: M. Ravindra, R. Srinivasa Rao

Abstract:

This paper presents a Generalized Binary Integer Linear Programming (GBILP) method for optimal allocation of Phasor Measurement Units (PMUs) and to generate Dynamic State Estimation (DSE) solution with complete observability. The GBILP method is formulated with Zero Injection Bus (ZIB) constraints to reduce the number of locations for placement of PMUs in the case of normal and single line contingency. The integration of PMU and conventional measurements is modeled in DSE process to estimate accurate states of the system. To estimate the dynamic behavior of the power system with proposed method, load change up to 40% considered at a bus in the power system network. The proposed DSE method is compared with traditional Weighted Least Squares (WLS) state estimation method in presence of load changes to show the impact of PMU measurements. MATLAB simulations are carried out on IEEE 14, 30, 57, and 118 bus systems to prove the validity of the proposed approach.

Keywords: Observability, phasor measurement units, PMU, state estimation, dynamic state estimation, SCADA measurements, zero injection bus.

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Authors: Teryima Oralu, Babatunde Kasim Oladele

Abstract:

This paper looks at the management and funding of education in Nigeria. The concept of management and administration has been concisely defined. Also the historical background of educational management in Nigeria has been discussed alongside the management of primary education, secondary education and tertiary education in Nigeria. Furthermore, the funding of education has also been concisely discussed in this paper alongside the various sources of funds available to education in Nigeria. The sources include government grant, school fees, external aids, school revenue yielding businesses and so on. The budgetary allocation of Nigeria to education from 1999 to 2013 was also highlighted in this in paper and it was discovered that the lowest allocation was in 1999 with 4.46% while the highest allocation was in 2006 with 10.43%. It is also of note that, Nigeria is still yet to meet the recommendation of UNESCO of 26% budgetary allocation to education by developing countries. Recommendations have been drawn that the government should increase budgetary allocation to this sector in a consistent manner because of its importance to the national economy, hoping that with proper monitoring of fund, it would contribute more significantly to the development of the country. An effective utilization of such funds is also advocated for greater achievements. All organs of the government should exhibit good corporate governance and transparency and so on.

Keywords: Education, funding, management, Nigeria.

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Authors: P. Keerthika, P. Suresh

Abstract:

Grid is an environment with millions of resources which are dynamic and heterogeneous in nature. A computational grid is one in which the resources are computing nodes and is meant for applications that involves larger computations. A scheduling algorithm is said to be efficient if and only if it performs better resource allocation even in case of resource failure. Resource allocation is a tedious issue since it has to consider several requirements such as system load, processing cost and time, user’s deadline and resource failure. This work attempts in designing a resource allocation algorithm which is cost-effective and also targets at load balancing, fault tolerance and user satisfaction by considering the above requirements. The proposed Budget Constrained Load Balancing Fault Tolerant algorithm with user satisfaction (BLBFT) reduces the schedule makespan, schedule cost and task failure rate and improves resource utilization. Evaluation of the proposed BLBFT algorithm is done using Gridsim toolkit and the results are compared with the algorithms which separately concentrates on all these factors. The comparison results ensure that the proposed algorithm works better than its counterparts.

Keywords: Grid Scheduling, Load Balancing, fault tolerance, makespan, cost, resource utilization.

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Authors: Kenichiro Hida, Shin-Ichi Kuribayashi

Abstract:

In a conventional network, most network devices, such as routers, are dedicated devices that do not have much variation in capacity. In recent years, a new concept of network functions virtualisation (NFV) has come into use. The intention is to implement a variety of network functions with software on general-purpose servers and this allows the network operator to select their capacities and locations without any constraints. This paper focuses on the allocation of NFV-based routing functions which are one of critical network functions, and presents the virtual routing function allocation algorithm that minimizes the total power consumption. In addition, this study presents the useful allocation policy of virtual routing functions, based on an evaluation with a ladder-shaped network model. This policy takes the ratio of the power consumption of a routing function to that of a circuit and traffic distribution between areas into consideration. Furthermore, the present paper shows that there are cases where the use of NFV-based routing functions makes it possible to reduce the total power consumption dramatically, in comparison to a conventional network, in which it is not economically viable to distribute small-capacity routing functions.

Keywords: Virtual routing function, NFV, resource allocation, minimum power consumption.

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Authors: M. Ravindra, R. Srinivasa Rao, V. Shanmukha Naga Raju

Abstract:

This paper presents state estimation with Phasor Measurement Unit (PMU) allocation to obtain complete observability of network. A matrix is designed with modeling of zero injection constraints to minimize PMU allocations. State estimation algorithm is developed with optimal allocation of PMUs to find accurate states of network. The incorporation of PMU into traditional state estimation process improves accuracy and computational performance for large power systems. The nonlinearity integrated with zero injection (ZI) constraints is remodeled to linear frame to optimize number of PMUs. The problem of optimal PMU allocation is regarded with modeling of ZI constraints, PMU loss or line outage, cost factor and redundant measurements. The proposed state estimation with optimal PMU allocation has been compared with traditional state estimation process to show its importance. MATLAB programming on IEEE 14, 30, 57, and 118 bus networks is implemented out by Binary Integer Programming (BIP) method and compared with other methods to show its effectiveness.

Keywords: Observability, phasor measurement units, synchrophasors, SCADA measurements, zero injection bus.

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Authors: Muhammad Abrar, Xiang Gui, Amal Punchihewa

Abstract:

In this paper we study the resource allocation problem for an OFDMA based cooperative two-way relaying (TWR) network. We focus on amplify and forward (AF) analog network coding (ANC) protocol. An optimization problem for two basic resources namely, sub-carrier and power is formulated for multi-user TWR networks. A joint optimal optimization problem is investigated and two-step low complexity sub-optimal resource allocation algorithm is proposed for multi-user TWR networks with ANC protocol. The proposed algorithm has been evaluated in term of total achievable system sum-rate and achievable individual sum-rate for each userpair. The good tradeoff between system sum-rate and fairness is observed in the two-step proportional resource allocation scheme.

Keywords: Relay Network, Relay Protocols, Resource Allocation, Two –way relaying.

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Authors: M.R. Ebrahimi, M. Ehsan

Abstract:

This paper presents a practical scheme that can be used for allocating the transmission loss to generators and loads. In this scheme first the share of a generator or load on the current through a branch is determined using Z-bus modified matrix. Then the current components are decomposed and the branch loss allocation is obtained. A motivation of proposed scheme is to improve the results of Z-bus method and to reach more fair allocation. The proposed scheme has been implemented and tested on several networks. To achieve practical and applicable results, the proposed scheme is simulated and compared on the transmission network (400kv) of Khorasan region in Iran and the 14-bus standard IEEE network. The results show that the proposed scheme is comprehensive and fair to allocating the energy losses of a power market to its participants.

Keywords: Transmission Loss, Loss Allocation, Z-bus modifiedmatrix, current Components Decomposition and Restructured PowerSystems

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Authors: Rooholah Hasanizadeh, Saadan Zokaei

Abstract:

In the context of sensor networks, where every few dB saving counts, the novel node cooperation schemes are reviewed where MIMO techniques play a leading role. These methods could be treated as joint approach for designing physical layer of their communication scenarios. Then we analyzed the BER performance of transmission diversity schemes under a general fading channel model and proposed a power allocation strategy to the transmitting sensor nodes. This approach is then compared to an equal-power assignment method and its performance enhancement is verified by the simulation. Another key point of the contribution lies in the combination of optimal power allocation and sensor nodes- cooperation in a transmission diversity regime (MISO). Numerical results are given through figures to demonstrate the optimality and efficiency of proposed combined approach.

Keywords: Optimal power allocation, cooperative MISO scheme, sensor networks, diversity branch.

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Authors: Vijaya K. Srivastava, Davide Spinello

Abstract:

This paper presents established 3ⁿ enumeration procedure for mixed integer optimization problems for solving multi-objective reliability and redundancy allocation problem subject to design constraints. The formulated problem is to find the optimum level of unit reliability and the number of units for each subsystem. A number of illustrative examples are provided and compared to indicate the application of the superiority of the proposed method.

Keywords: Integer programming, mixed integer programming, multi-objective optimization, reliability redundancy allocation.

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Authors: A. Safari, R. Jahani, H. A. Shayanfar, J. Olamaei

Abstract:

This paper shows the results obtained in the analysis of the impact of distributed generation (DG) on distribution losses and presents a new algorithm to the optimal allocation of distributed generation resources in distribution networks. The optimization is based on a Hybrid Genetic Algorithm and Particle Swarm Optimization (HGAPSO) aiming to optimal DG allocation in distribution network. Through this algorithm a significant improvement in the optimization goal is achieved. With a numerical example the superiority of the proposed algorithm is demonstrated in comparison with the simple genetic algorithm.

Keywords: Distributed Generation, Distribution Networks, Genetic Algorithm, Particle Swarm Optimization.

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Authors: Cuiran Li, Jianli Xie, Chengshu Li

Abstract:

Multicarrier code-division multiple-access is one of the effective techniques to gain its multiple access capability, robustness against fading, and to mitigate the ISI. In this paper, we propose an improved mulcarrier CDMA system with adaptive subchannel allocation. We analyzed the performance of our proposed system in frequency selective fading environment with narrowband interference existing and compared it with that of parallel transmission over many subchannels (namely, conventional MC-CDMA scheme) and DS-CDMA system. Simulation results show that adaptive subchannel allocation scheme, when used in conventional multicarrier CDMA system, the performance will be greatly improved.

Keywords: MC-CDMA, Rayleigh fading, Narrowbandinterference, Channel estimation.

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Authors: Kemal Bicakci, Yusuf Uzunay

Abstract:

It is well-known that in wireless local area networks, authenticating nodes by their MAC addresses is not secure since it is very easy for an attacker to learn one of the authorized addresses and change his MAC address accordingly. In this paper, in order to prevent MAC address spoofing attacks, we propose to use dynamically changing MAC addresses and make each address usable for only one session. The scheme we propose does not require any change in 802.11 protocols and incurs only a small performance overhead. One of the nice features of our new scheme is that no third party can link different communication sessions of the same user by monitoring MAC addresses therefore our scheme is preferable also with respect to user privacy.

Keywords: Authentication, MAC address spoofing, security, wireless networks.

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Authors: Lu Yanhui, Zhang Lizhi, Yin Changchuan, Yue Guangxin

Abstract:

In this paper, an adaptive radio resource allocation (RRA) algorithm applying to multiple traffic OFDMA system is proposed, which distributes sub-carrier and loading bits among users according to their different QoS requirements and traffic class. By classifying and prioritizing the users based on their traffic characteristic and ensuring resource for higher priority users, the scheme decreases tremendously the outage probability of the users requiring a real time transmission without impact on the spectrum efficiency of system, as well as the outage probability of data users is not increased compared with the RRA methods published.

Keywords: OFDMA, adaptive radio resource allocation, QoS.

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Authors: Fatima Z. Cherhabil, Mammar Sedrati, Sonia-Sabrina Bendib‎

Abstract:

In order to support the continued growth, critical latency of ‎IoT ‎applications and ‎various obstacles of traditional data centers, ‎Mobile Edge ‎Computing (MEC) has ‎emerged as a promising solution that extends the cloud data-processing and decision-making to edge devices. ‎By adopting a MEC structure, IoT applications could be executed ‎locally, on ‎an edge server, different fog nodes or distant cloud ‎data centers. However, we are ‎often ‎faced with wanting to optimize conflicting criteria such as ‎minimizing energy ‎consumption of limited local capabilities (in terms of CPU, RAM, storage, bandwidth) of mobile edge ‎devices and trying to ‎keep ‎high performance (reducing ‎response time, increasing throughput and service availability) ‎at the same ‎time‎. Achieving one goal may affect the other making Task Offloading (TO), ‎Resource Allocation (RA) and Service Placement (SP) complex ‎processes. ‎It is a nontrivial multi-objective optimization ‎problem ‎to study the trade-off between conflicting criteria. ‎The paper provides a survey on different TO, SP and RA recent Multi-‎Objective Optimization (MOO) approaches used in edge computing environments, particularly Artificial Intelligent (AI) ones, to satisfy various objectives, constraints and dynamic conditions related to IoT applications‎.

Keywords: Mobile Edge Computing, Multi-Objective Optimization, Artificial Intelligence ‎Approaches, Task Offloading, Resource Allocation, Service Placement‎.

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Authors: W.S. Lim, M.V.C. Rao

Abstract:

In this paper, the processing of sonar signals has been carried out using Minimal Resource Allocation Network (MRAN) and a Probabilistic Neural Network (PNN) in differentiation of commonly encountered features in indoor environments. The stability-plasticity behaviors of both networks have been investigated. The experimental result shows that MRAN possesses lower network complexity but experiences higher plasticity than PNN. An enhanced version called parallel MRAN (pMRAN) is proposed to solve this problem and is proven to be stable in prediction and also outperformed the original MRAN.

Keywords: Ultrasonic sensing, target classification, minimalresource allocation network (MRAN), probabilistic neural network(PNN), stability-plasticity dilemma.

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Authors: Simon Samwel Msanjila

Abstract:

Networked environments which provide platforms for business organizations are configured in different forms depending on many factors including life time, member characteristics, communication structure, and business objectives, among others. With continuing advances in digital technologies the distance has become a less barrier for business minded collaboration among organizations. With the need and ease to make business collaborate nowadays organizations are sometimes forced to co-work with others that are either unknown or less known to them in terms of history and performance. A promising approach for sustaining established collaboration has been establishment of trust relationship among organizations based on assessed trustworthiness for each participating organization. It has been stated in research that trust in organization is dynamic and thus assessment of trust level must address such dynamic nature. This paper assesses relevant aspects of trust and applies the assessed concepts to propose a semi-automated system for the management of Sustainability and Evolution of trust in organizations participating in specific objective in a networked organizations environment.

Keywords: Trust evolution, trust sustainability, networked organizations, dynamic trust.

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Authors: Wookuen Shin, Gregory R. Miller, Pedro Arduino, Peter Mackenzie-Helnwein

Abstract:

This paper presents strategies for dynamically creating, managing and removing mesh cells during computations in the context of the Material Point Method (MPM). The dynamic meshing approach has been developed to help address problems involving motion of a finite size body in unbounded domains in which the extent of material travel and deformation is unknown a priori, such as in the case of landslides and debris flows. The key idea is to efficiently instantiate and search only cells that contain material points, thereby avoiding unneeded storage and computation. Mechanisms for doing this efficiently are presented, and example problems are used to demonstrate the effectiveness of dynamic mesh management relative to alternative approaches.

Keywords: Numerical Analysis, Material Point Method, Large Deformations, Moving Boundaries.

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Authors: Hassan Haghighi, Seyedeh Zahra Hosseini, Seyedeh Elahe Jalambadani

Abstract:

One of the most important aspects expected from an ERP system is to mange user\administrator manual documents dynamically. Since an ERP package is frequently changed during its implementation in customer sites, it is often needed to add new documents and/or apply required changes to existing documents in order to cover new or changed capabilities. The worse is that since these changes occur continuously, the corresponding documents should be updated dynamically; otherwise, implementing the ERP package in the organization encounters serious risks. In this paper, we propose a new architecture which is based on the agent oriented vision and supplies the dynamic document generation expected from ERP systems using several independent but cooperative agents. Beside the dynamic document generation which is the main issue of this paper, the presented architecture will address some aspects of intelligence and learning capabilities existing in ERP.

Keywords: enterprise resource planning, dynamic documentgeneration, software architecture, agent oriented architecture, learning, intelligence

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Authors: Kalyani J. Kulkarni, Bharat S. Chaudhari

Abstract:

This paper addresses the issue of resource allocation in the emerging cognitive technology. Focusing the Quality of Service (QoS) of Primary Users (PU), a novel method is proposed for the resource allocation of Secondary Users (SU). In this paper, we propose the unique Utility Function in the game theoretic model of Cognitive Radio which can be maximized to increase the capacity of the Cognitive Radio Network (CRN) and to minimize the interference scenario. Utility function is formulated to cater the need of PUs by observing Signal to Noise ratio. Existence of Nash Equilibrium for the postulated game is established.

Keywords: Cognitive Networks, Game Theory, Nash Equilibrium, Resource Allocation.

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Authors: H. Ashrafi, S. Ebrahimi, H. Kamalzadeh

Abstract:

With the development of business competition, it is important for healthcare providers to improve their service qualities. In order to improve service quality of a clinic, four important dimensions are defined: tangibles, responsiveness, empathy, and reliability. Moreover, there are several service stages in hospitals such as financial screening and examination. One of the most challenging limitations for improving service quality is budget which impressively affects the service quality. In this paper, we present an approach to address budget uncertainty and provide guidelines for service resource allocation. In this paper, a service quality improvement approach is proposed which can be adopted to multistage service processes to improve service quality, while controlling the costs. A multi-objective function based on the importance of each area and dimension is defined to link operational variables to service quality dimensions. The results demonstrate that our approach is not ultra-conservative and it shows the actual condition very well. Moreover, it is shown that different strategies can affect the number of employees in different stages.

Keywords: Service quality assessment, healthcare resource allocation, robust optimization, budget uncertainty.

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Authors: M.R. Ebrahimi, Z. Ghofrani, M. Ehsan

Abstract:

One of the major problems in liberalized power markets is loss allocation. In this paper, a different method for allocating transmission losses to pool market participants is proposed. The proposed method is fundamentally based on decomposition of loss function and current projection concept. The method has been implemented and tested on several networks and one sample summarized in the paper. The results show that the method is comprehensive and fair to allocating the energy losses of a power market to its participants.

Keywords: Transmission loss, loss allocation, current projectionconcept, loss function decomposition.

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Authors: K. Balamurugan, R. Muralisachithanandam, V. Dharmalingam, R. Srikanth

Abstract:

This paper deals with the optimal choice and allocation of multi FACTS devices in Deregulated power system using Evolutionary Programming method. The objective is to achieve the power system economic generation allocation and dispatch in deregulated electricity market. Using the proposed method, the locations of the FACTS devices, their types and ratings are optimized simultaneously. Different kinds of FACTS devices are simulated in this study such as UPFC, TCSC, TCPST, and SVC. Simulation results validate the capability of this new approach in minimizing the overall system cost function, which includes the investment costs of the FACTS devices and the bid offers of the market participants. The proposed algorithm is an effective and practical method for the choice and allocation of FACTS devices in deregulated electricity market environment. The standard data of IEEE 14 Bus systems has been taken into account and simulated with aid of MAT-lab software and results were obtained.

Keywords: FACTS devices, Optimal allocation, Deregulated electricity market, Evolutionary programming, Mat Lab.

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Authors: Amir Mohammad Fathollahi Fard, Mostafa Hajiaghaei-Keshteli, Mohammad Mahdi Paydar

Abstract:

With increasing life expectancy in developed countries, the role of home care services is highlighted by both academia and industrial contributors in Home Health Care Supply Chain (HHCSC) companies. The main decisions in such supply chain systems are the location of pharmacies, the allocation of patients to these pharmacies and also the routing and scheduling decisions of nurses to visit their patients. In this study, for the first time, an integrated model is proposed to consist of all preliminary and necessary decisions in these companies, namely, location-allocation-routing model. This model is a type of NP-hard one. Therefore, an Imperialist Competitive Algorithm (ICA) is utilized to solve the model, especially in large sizes. Results confirm the efficiency of the developed model for HHCSC companies as well as the performance of employed ICA.

Keywords: Home health care supply chain, location-allocation-routing problem, imperialist competitive algorithm, optimization.

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Authors: A. Al-Rifaie, Z. W. Guan, S. W. Jones

Abstract:

This paper presents a method for modelling and analysing end plate beam-to-column connections to obtain the quasi-static behaviour using non-linear dynamic explicit integration. In addition to its importance to study the static behaviour of a structural member, quasi-static behaviour is largely needed to be compared with the dynamic behaviour of such members in order to investigate the dynamic effect by proposing dynamic increase factors (DIFs). The beam-to-column bolted connections contain various contact surfaces at which the implicit procedure may have difficulties converging, resulting in a large number of iterations. Contrary, explicit procedure could deal effectively with complex contacts without converging problems. Hence, finite element modelling using ABAQUS/explicit is used in this study to address the dynamic effect may be produced using explicit procedure. Also, the effect of loading rate and mass scaling are discussed to investigate their effect on the time of analysis. The results show that the explicit procedure is valuable to model the end plate beam-to-column connections in terms of failure mode, load-displacement relationships. Also, it is concluded that loading rate and mass scaling should be carefully selected to avoid the dynamic effect in the solution.

Keywords: Quasi-static, end plate, finite element, connections.

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Authors: M. Sedighizadeh, A. Rezazadeh

Abstract:

This paper presents a method for the optimal allocation of Distributed generation in distribution systems. In this paper, our aim would be optimal distributed generation allocation for voltage profile improvement and loss reduction in distribution network. Genetic Algorithm (GA) was used as the solving tool, which referring two determined aim; the problem is defined and objective function is introduced. Considering to fitness values sensitivity in genetic algorithm process, there is needed to apply load flow for decision-making. Load flow algorithm is combined appropriately with GA, till access to acceptable results of this operation. We used MATPOWER package for load flow algorithm and composed it with our Genetic Algorithm. The suggested method is programmed under MATLAB software and applied ETAP software for evaluating of results correctness. It was implemented on part of Tehran electricity distributing grid. The resulting operation of this method on some testing system is illuminated improvement of voltage profile and loss reduction indexes.

Keywords: Distributed Generation, Allocation, Voltage Profile, losses, Genetic Algorithm.

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Authors: María S. Avila-García, John N. Carter, Robert I. Damper

Abstract:

An important problem in speech research is the automatic extraction of information about the shape and dimensions of the vocal tract during real-time speech production. We have previously developed Southampton dynamic magnetic resonance imaging (SDMRI) as an approach to the solution of this problem.However, the SDMRI images are very noisy so that shape extraction is a major challenge. In this paper, we address the problem of tongue shape extraction, which poses difficulties because this is a highly deforming non-parametric shape. We show that combining active shape models with the dynamic Hough transform allows the tongue shape to be reliably tracked in the image sequence.

Keywords: Vocal tract imaging, speech production, active shapemodels, dynamic Hough transform, object tracking.

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Authors: H. T. Barney, G. C. Low

Abstract:

The design of distributed systems involves dividing the system into partitions (or components) and then allocating these partitions to physical nodes. There have been several techniques proposed for both the partitioning and allocation processes. These existing techniques suffer from a number of limitations including lack of support for replication. Replication is difficult to use effectively but has the potential to greatly improve the performance of a distributed system. This paper presents a new technique technique for allocating objects in order to improve performance in a distributed system that supports replication. The performance of the proposed technique is demonstrated and tested on an example system. The performance of the new technique is compared with the performance of an existing technique in order to demonstrate both the validity and superiority of the new technique when developing a distributed system that can utilise object replication.

Keywords: Allocation, Distributed Systems, Replication.

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Authors: Mihails Kulikovs, Ernests Petersons

Abstract:

Network management techniques have long been of interest to the networking research community. The queue size plays a critical role for the network performance. The adequate size of the queue maintains Quality of Service (QoS) requirements within limited network capacity for as many users as possible. The appropriate estimation of the queuing model parameters is crucial for both initial size estimation and during the process of resource allocation. The accurate resource allocation model for the management system increases the network utilization. The present paper demonstrates the results of empirical observation of memory allocation for packet-based services.

Keywords: Queuing System, Packet Loss Probability, Measurement-Based Admission Control (MBAC), Performanceevaluation, Quality of Service (QoS).

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Authors: Gee-Cheol Kim, Sang-Hoon Lee, Joo-Won Kang

Abstract:

In the stadium structure, the significant dynamic responses such as resonance or similar behavior can be occurred by spectator rhythmical activities. Thus, accurate analysis and precise investigation of stadium structure that is subjected to dynamic loads are required for practical design and serviceability check of stadium structures. Moreover, it is desirable to measure and analyze the dynamic loads of spectator activities because these dynamic loads can not be easily expressed in numerical formula. In this study, various dynamic loads induced by spectator movements are measured and analyzed. These dynamic loads induced by spectators movement of stadium structure can be classified into the impact load and the periodic load. These dynamic loads can be expressed as Fourier harmonic load. And, these dynamic loads could be applied for the accurate vibration analysis of a stadium structure.

Keywords: stadium structure, spectator rhythmical activities, vibration analysis.

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Authors: Kazuhisa Takagi

Abstract:

This paper is about movies and dynamic objects for mobile phones. Dynamic objects are the software programmed by JavaScript. They consist of geometric figures and work on HTML5-compliant browsers. Mobile phones are very popular among teenagers. They like watching movies and playing games on them. So, mathematics movies and dynamic objects would enhance teaching and learning processes. In the movies, manga characters speak with artificially synchronized voices. They teach trigonometry together with dynamic mathematical objects. Many movies are created. They are Windows Media files or MP4 movies. These movies and dynamic objects are not only used in the classroom but also distributed to students. By watching movies, students can study trigonometry before or after class.

Keywords: Dynamic mathematical object, JavaScript, Google drive, transfer jet.

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